Question

5 Folosind formula de calcul pentru pătratul unei
sume algebrice, calculaţi:
a) (x²+2y)²;
b) (4x-3y)²;
c) (√2x+√3)²; d) (x - √√5y)².
2
2
0) (1 x - y)²; 9 (x + 1) ².
e)
2
Folosind formula de calcul pentru produsu

Answer 1

Răspuns:

a.

$( {x}^{2} + 2y) ^{2}$

$( {x}^{2} ) ^{2} + 2x^{2} \times 2y + (2y) ^{2}$

${x}^{4} + 2x ^{2} + 2y + (2y) ^{2}$

${x}^{4} + 4x ^{2} y + (2y) ^{2}$

$x ^{4} + 4x ^{2} y + 4y ^{2}$

$x ^{4} + 4x ^{2} y + 4y ^{2}$

b.

$(4x - 3y) ^{2}$

$(4x) ^{2} - 2 \times 4x \times 3y + (3y) ^{2}$

$16 x ^{2} - 2 \times 4x \times 3y + (3y) ^{2}$

$16x ^{2} - 24xy + (3y)^{2}$

$16x ^{2} - 24xy + 9y ^{2}$

$16x ^{2} - 24xy + 9y ^{2}$

c.

$( \sqrt{2x} + \sqrt{3} ) ^{2}$

$\sqrt{2x} ^{2} + 2 \sqrt{2x} \sqrt{3} + \sqrt{3} ^{2}$

$2x + 2 \sqrt{2x} \sqrt{3} + \sqrt{3 ^{2} }$

$2x + 2 \sqrt{6x} + \sqrt{3} ^{2}$

$2 \times + 2 \sqrt{6x} + 3$

$2 \times + 2 \sqrt{6x} + 3$

d.

$(x - \sqrt{5y} ) ^{2}$

$x^{2} - 2x \sqrt{5y} + \sqrt{5y} ^{2}$

${x}^{2} - 2x \sqrt{5y} + 5y$

${x}^{2} - 2x \sqrt{5y} + 5y$

e.

$2 = \frac{1}{2}$

Explicație pas cu pas:

sper că te-am ajutat :)